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A Note on Generating Almost Pythagorean Triples

2015/08/30 by John Rafael M. Antalan, Antalan, John Rafael M., Mark D. Tomenes +1
Mathematics · #11A99 #11D45 #Advanced Mathematical Theories #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1508.07562

openalex publication_date 2015/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1987, Orrin Frink introduced the concept of almost Pythagorean triples. He defined them as an ordered triple (x,y,z) that satisfies the equation x2+y2=z2+1 where x,y and z are positive integers. In his paper, he showed that there were infinitely many almost Pythagorean triples by giving a characterization which suggests a method on generating all of them. However, this method does not explicitly and readily give a particular almost Pythagorean triple. In this note, using basic algebraic operations, we extend his result by giving a characterization that explicitly and readily give a particular almost Pythagorean triple.

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